DAT Bootcamp - Quantitative Reasoning
how much is each quartile in a box and whisker plot?
25%
what is the value of pi?
3.14
what is the volume of a sphere?
4/3πr^3
how many grams are in a pound?
454 grams
surface area of a sphere
4πr²
an angle and it's complement sum to
90°
how much of the data in a normal distribution is two standard deviations from your average?
95%
how do you solve a dilution problem?
C1V1=C2V2
what is the percent increase formula?
F - I / I x100
Pythagorean Theorem
a²+b²=c²
what is the distance formula for 2 points on a graph?
d = √(x2 - x1)^2 + (y2 - y1)^2
what is the mode?
most frequently occurring value
volume of a cube
s^3
when you are given a ratio, you need to determine
the scale by converting the ratio to something like 2x:9x then solve for x.
what is the area of a circle?
πr^2
inches to cm
1 inch = 2.54 cm
yards to meters
1 yd = 0.914 m
how do you find the standard deviation of a data set?
1. square the distance each value is from the median 2. add the values together, and divide by the number of values there are 3. take the square root
what is the combined work formula and how to you solve?
1/person A time + 1/person B time = 1 / x (time together) to solve you need to find the least common multiple of the two fractions and solve for t
how many digits are there?
10
how many mm in cm?
10
how many centimeters in a meter?
100 (1 x 10^2)
cm to m
100 cm = 1 m
how many mL in liter?
1000
how many meters are in a mile?
1609 meters
what is the sum of internal angles formula? how do you find one angle in the shape using this?
180(n-2) = sum of internal angles sum of internal angles / n = one angle in the shape
how do you solve a problem when given a set of integers as a ratio and a sum?
1k + 2k + 7k = 79 k is the scaling factor
b² - 4ac > 0
2 real roots
how many kg are in a pound?
2.2 kg
when you are given a ratio that CHANGES, what do you do? for example, 7:3 changing to 5:3 by the first part of the ratio (7) giving 2 to the bottom part of the ratio (3)
7x - 2 5 ------- = --- 3x + 2 3
area of a triangle in a rectangle split in two
A=1/2bh
What is the area of a parallelogram?
A=bh
When do you flip an inequality symbol?
Anytime you multiply or divide by a NEGATIVE number.
what is the volume of a cylinder?
V=πr^2h
z-score
a measure of how many standard deviations you are away from the norm
how do you find the number of coins given the values of the coins and total amount of money?
move the decimal 2 spots to the left. make a formula using the value of the coin, examples: MAKE SURE YOU INCORPORATE THE FORMULA: 5N + 10D + 25Q + 1P = TOTAL MOVED TWO PLACES 5N + P = amount moved two places 25Q + 10D = amount moved two places
what combination formula do you use when order matters?
n! / (n-k)!
what is the combination formula when order does not matter? (which is most cases)
n! / (n-r)! r!
b² - 4ac < 0
no real roots
if the values from the original sample are doubled, how will the standard deviation and mean change?
the mean will double and the standard deviation will double
if over half of a data set are the same number, what must also be the same as this number?
the median and mode
when two x and y values are swapped in a system of equations and they equal the same thing, what does this mean?
the two systems of equations are equal
how would the mean, SD, and median change if divided?
they would all decrease
What is the interquartile range?
top of the box MINUS the bottom of the box
how do you solve a GPA question?
total grade points / # of credits taken # of credits = how many credits each class is worth, the actual grade credits the question gave you grade points = grade credits x the actual grade
deci
10^-1
what is the circumference of a circle?
2πr
what is the surface area of a cylinder?
2πr² + 2πrh
feet to yards
3 ft = 1 yd
how much of the data in a normal distribution is one standard distribution from your average?
68%
surface area of a cube
6s^2
when you are solving an age problem that says "in 3 years, dana will be double Alex's age" what will the formula be?
D+3 = 2(A+3) ----> D+3 = 2A+6
centi
10^-2
milli
10^-3
kilo
10^3
how much of the data in a normal distribution is three standard deviations from your average
99.7%
what is the compound growth (interest) formula?
A = P( 1 + r/n) ^nt A = final P = present r = rate n = compound t = time in YEARS
when are fractions undefined?
denominator = 0
how do you find how many ways letters can be arranged?
divide the total number of letters by the repeating letters. example: APPALOOSA 9 total letters, 3 repeating letters (3A, 2P, 2O) 9! ------ 3! 2! 2!
what does G∪F mean?
every number in the set must be present in both G and F
b² - 4ac = 0
one root
arranged
order matters
